Transcript Two-Way Frequency Tables

Algebra 1 - Functions:
Interpret & Building
Functions
Unit 5
Purpose
Provided is a lesson for teachers to use to help students understand
and analyze bivariate data. Included are the following:
Standards
Statistics and
Probability
Learning
Progression
Getting Ready
for the Lesson
(Resources and
Tips)
Vocabulary
Activities
Textbook
Connections
Lesson Agenda
Lesson
(Online and
Interactive)
Additional
Resources
Common Core Standards
F.IF.4 For a function that models a relationship
between two quantities, interpret key features of
graphs and tables in terms of the quantities, and
sketch graphs showing key features given a
verbal description of the relationship.
F.IF.5 Relate the domain of a function to its graph
and, where applicable, to the quantitative
relationship it describes.
(Analyze, 2) (Understand, 2) (Apply, 2)
Math Practices
MP1
• Make sense of problems and persevere in solving them.
MP3
• Construct viable arguments & critique the reasoning of
others.
MP4
• Model with mathematics
MP5
• Use appropriate tools strategically
Functions
Prerequisite Skills: CC Math 8
http://commoncoretools.me/wp-content/uploads/2013/07/ccss_progression_functions_2013_07_02.pdf
Middle School Focus
Grade 6
Grade 7
Grade 8
O Understand
O Analyze
O Understand
ratio concepts
and use ratio
reasoning to
solve problems
proportional
relationships and
use them to solve
real-world and
mathematical
problems
Source: California Framework
the
connections
between
proportional
relationships,
lines, and
linear
equations.
High School Focus
Algebra I
 Interpret functions that





arise in applications in
terms of a context
Analyze functions using
different representations.
Build a function that
models a relationship
between two quantities.
Build new functions from
existing functions
Construct and compare
linear, quadratic, and
exponential models and
solve problems
Interpret expressions for
functions in terms of the
situation they mode.
Geometry
 Use coordinates
to prove simple
geometric
theorems
algebraically
Algebra II
 Interpret functions that




arise in applications in
terms of a context
Analyze functions using
different
representations.
Build a function that
models a relationship
between two
quantities.
Build new functions
from existing functions
Construct and
compare linear,
quadratic, and
exponential models
and solve problems
Source: California Framework
Learning Progression:
HS Functions
http://commoncoretools.me/wp-content/uploads/2013/07/ccss_progression_functions_2013_07_02.pdf
Lesson Agenda
O Vocabulary
O Lesson: Incline Interactive Tool
O Textbook Connections
Motor Cross Incline
Planning for Instruction with Interpreting
Functions
Getting Ready
O Pre-assessment- used to determine
understanding of prerequisite skills
O Prerequisite skills include
O 7 RP 1 – 3
O Analyze Proportional Relationships.
O Solve Real World Mathematical Problems.
O8F1–3
O Define, Evaluate and Compare Functions
Misconceptions and Anticipated
Issues
Common Issues
O Students may assume that
all linear graphs go through
the origin.
O How movement of real-life
objects affect function
representation.
Suggested Strategies/Resources
O What distinguishing
characteristics do you notice in
the graphs? tables? equations?
O How do these help you?
O How do each of the
representations compare to each
other?
O How can you represent your
ideas so that everyone can
understand them?
Required Resources
Materials Required
Special Materials:
O Access to the Internet
http://www.shodor.org/interactivate/activities/Incline/
Handouts from Website:
O Exploration Questions
O Activity Function Flyer
O Activity Function Machine
O Activity Linear Function Machine
O Activity Positive Linear Function Machine
O Discussion about Independent and Dependent Variables
O Worksheet Incline Exploration Questions
Needed Vocabulary
O Function
O Dependent Variables
O Rate of Change
O Quadratic
O Independent
O Exponential
Variables
O Linear
Frayer’s
Model
Or you could
use: Word
Map, Layered
Book, etc.
Demonstrating the relationship between
dependent and independent variables
http://www.shodor.org/interactivate/activities/Incline/
Planning and Time
Activities
Time
Notes
Preparation
1 hours
Includes creating a preassessment, making copies,
obtaining materials
Pre-lessons
30 min
Review of 7th and/or 8th
grade SP standards
Vocabulary
1 hour
Defining Function, Rate of
Change, Independent &
Dependent Variable
Motor Cross Incline
2 hours
Interactive Activity
Practice and Additional
Tasks
2 hours
Additional worksheets from
shodor.org
Total Time
6.5 hours
Textbook Connection
Big Ideas
O Lessons:
O 3.2 Linear Functions
O 3.5 Graphing Linear Equations in Slope-Intercept Form
O 6.3 Exponential Functions
O 8.4 Graphing
O 8.5 Using Intercept Form
O 9.2 Solving Quadratic Equations by Graphing
O 10.1 Graphing Square Root Functions
O 10.2 Graphing Cube Root Functions
Textbook Connection
Spring Board
O Lessons:
O 7-1 The Spring Experiment
O 7-2 The Falling Object Experiment
O 7-3 The Radioactive Decay Experiment
O 11-1 Identifying Arithmetic Sequence
O 11-2 Point-Slope From
O 11-3 Standard Form
O 11-4 Recursive Formulas
O 29-1 Modeling with a Quadratic Functions
O 29-2 Graphing and Analyzing a Quadratic Function
O 30-1 Translations of the Quadratic parent Functions
O 30-2 Stretching and Shrinking the Quadratic Parent Function
O 30-3 Multiple Transformation of the Quadratic Parent Function
O 33-1 Fitting Data with a Quadratic Function
O 33-2 Interpreting Solutions of Quadratic Equations
Textbook Connection
CPM
O Lessons:
O 1.1.3, 1.2.1, 1.2.4-1.2.5
O 2.1.3–2.2.3
O 7.1.1, 7.1.5-7.2.1
O 8.2.1, 8.2.3, 8.2.4
O 11.3.2-11.3.4, 11.3.5
Additional Resources
O Illustrative Mathematics -
www.illustrativemathematics.com
O
O
O
O
O
O
O
O
Influenza Epidemic
Warming and Cooling
How is the Weather?
Logistic Growth Model, Explicit Version
The Canoe Trip, Variation 1
The High School Gym
Temperature Change
Average Cost
O Khan Academy - www.khanacademy.org
O Engage NY Common Core Curriculum
O Math Assessment Project – map.mathshell.org
Need Help?
Contact your
Secondary Math Coordinator